Conditionality Properties for the Bivariate Logarithmic Distribution with an Application to Goodness of Fit
The paper gives new modes of genesis for the multivariate and homogeneous bivariate logarithmic distributions. Marginality and conditionality properties are derived (including, e.g., X|Y > X, X|Y - X = n), and are applied to the problem of grouping frequencies for a chi-square goodness-of-fit test for the homogeneous bivariate logarithmic distribution. The proposed procedure is objective and impartial with respect to rows and columns.
Key WordsBivariate logarithmic series distribution multivariate logarithmic series distribution modes of genesis chi-squared goodness-of-fit objective grouping homogeneous distributions
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- Boswell, M.T., Patil, G.P., (1971). Chance mechanisms generating the logarithmic series destribution used in the analysis of number of species and individuals. In Statistical Ecology, Vol. 1 G.P. Patil et al The Pennsylvania state University Press, University Park. Pages 99–130Google Scholar
- Kemp, A.W. (1981). Frugal methods of generating bivariate discrete random variables. In Statistical Distributions in Scientific Work, C. Taillie, G. P. Patil, B. Baldessari, eds. Reidel, Dordrecht-Holland. Vol. 4, 321–329.Google Scholar
- Kemp, A.W. (1981). Efficient generation of the logarithmic distribution. Applied Statistics (in press).Google Scholar
- McCloskey, J.W. (1965). A model for the distribution of individuals by species in an environment. Technical Report No. 7, Department of Statistics, Michigan State University.Google Scholar
- Nelson, W.C., David, H.A. (1967). The logarithmic distribution: a review. Virginia Journal of Science, 18, 95–102.Google Scholar
- Neyman, J. (1965). Certain chance mechanisms involving discrete distributions. In Classical and Contagious Discrete Distributions, G. P. Patil, ed. Pergamon Press, London. Pages 4–14.Google Scholar
- Subrahmanian, K. (1966). A test for “intrinsic correlation” in the theory of accident proneness. Journal of the Royal Statistical Society, Series B, 28, 180–189.Google Scholar